Cpk is short for Process Capability Index, and describe if a process is capable. Process capability is the ability of a process to make a feature within its tolerance.

Before running a Cpk, the process should be in control. This can be determined with Statistical Process Control (SPC).

## Cpk and Variation

Everything varies, and the variation can be seen if we measure precisely enough

- Heights
- Weights
- Lengths
- Widths
- Diameters
- Horsepower
- Miles per Gallon
- Pressure
- Roughness
- Strength
- Speed
- Torque

## Cpk Tolerance and Measurement

It’s useful to see the tolerance and the part measurement on a graph.

Suppose that:

- The tolerance is .515” to .525”
- An individual part is measured at .520”.

Suppose we made and measured several more units, and they were all EXACTLY the same!

If that were the case, then we wouldn’t have very many part problems.

In the real world, units are not exactly the same, everything varies. The question isn’t if units vary, but how much, when, and why.

## Cpk the Normal Bell Curve

Widths, heights, depths, thicknesses, weights, speeds, strengths, and many other types of measurements, when charted as a histogram, often form the shape of a bell.

A perfect bell, like a perfect circle doesn’t occur in nature, but many processes are close enough to make the bell curve useful.

## Cpk and Standard Deviation

If we measure the distance from the center of the bell to each individual measurement that makes up the bell curve, we can find a typical distance.

The most commonly used statistic to estimate this distance is the Standard Deviation (also called “Sigma”). Because of the natural shape of the bell curve, the area of +1 to –1 standard deviations includes about 68% of the curve.

How much of the curve is included in how many standard deviations?

- From –1 to +1 is about 68% of the bell curve.
- From –2 to +2 is about 95%
- From –3 to +3 is about 99.73%
- From –4 to +4 is about 99.99%

NOTE: We usually show the bell from –3 to +3 to make it easier to draw, but in concept, the tails of the bell get very thin and go on forever.

## What is Cpk

It is a measure of how well a process is within a specification.

Cpk = A divided by B

- A = Distance from process mean to closest spec limit
- B = 3 Standard Deviations (also called “3 Sigma”)

A bigger Cpk is better because fewer units will be beyond spec. A bigger “A” and a smaller “B” are better and means a better process capability.

In order to improve the Cpk following can be done

- Design the product so a wider tolerance is functional (robust design)
- Choose equipment and methods for a good safety margin (process capability)
- Correctly adjust, but only when needed (control)
- Discover ways to narrow the natural variation (improvement)

The above process is producing good units with a good safety margin with a Cpk around 2. Note that when Cpk = 2, our process mean is 6 standard deviations from the nearest spec, so we say it has Six Sigma Capability.

Usually we desire a minimum Cpk of 1.33 and ultimately we want 2 or more.

Below is an example of a process with a very Cpk (below 1), and a significant part of the tail is hanging out beyond the spec limits. This process is producing scrap, rework, and customer rejects.

If you are interested in Cpk, then our 8D Problem Solving Training or SPC Training might be interesting for you.

Our 8D Training is a detailed training on how to effectively solve problems and prevent them from reoccurring, and the SPC Training looks at process control and continuous improvement. They both cover the use of Cpk as part of the training.

Alternatively you can continue to our quality training page for an overview of the training we provide.

Go to Quality Training